DEDHAM — Talks resumed between striking teachers and school administrators on a long-sought contract Saturday afternoon, shortly after throngs of of educators, school staff, and their supporters marched to a school athletic field to ­demand a new agreement.

Members of the Dedham ­Education Association voted overwhelmingly Thursday to strike, following nearly two years of contract talks that stalled in August.

Tim Dwyer, president of the union, told hundreds gathered for an early afternoon rally that he was optimistic a deal could be reached but sounded a defiant note if the strike had to continue.

“I have hope we will negotiate today in good faith, and that we will come out of it with a contract,’’ he told the crowd.

Teachers’ strikes are illegal in Massachusetts, and Dedham Superintendent Michael Welch released a statement Thursday that said the state Department of Labor Relations issued a decision that called on strikers to return to work.

The department’s Commonwealth Employment Relations Board ruling ordered the union to “immediately cease and desist from engaging or threatening to engage in a strike or work stoppage, slowdown, or other withholding of services.’’

Rachel Dudley, chairwoman of the association’s negotiating team, acknowledged Saturday morning that the strike was illegal but said “it is not criminal.’’

During the rally, Dwyer told the crowd that violating that law would result in little more than a fine.

“Until we have a fair contract, we do not open the Dedham Public Schools,’’ he said.

Welch, in a phone interview Saturday, called the strike a “sad situation’’ and said administrators want to work quickly to reach a deal.

It’s critical that teachers resume work, he said, because of the needs of students, including those preparing for college and participating in athletics.

“We love our teachers, our teachers are very hard working, our teachers deserve fair compensation, and they deserve a fair contract,’’ Welch said.

Union members are seeking salary increases and changes in how the district configures its health plan, as well as cellphone use by students in schools.

The union also wants changes in sexual harassment issues, including the introduction of a policy in the contract on the administration’s handling of sexual harassment of teachers by students. It also seeks to allow union members to take sexual harassment complaints through a grievance procedure for redress.

The Dedham Education Association voted 275 to 2 in favor of a strike Thursday. The strike vote included teachers, nurses, school psychologists, and counselors. The association also represents paraprofessionals, cafeteria workers, and a small number of administrators who are in different units of the union that are not on strike.

On Saturday, hundreds marched about a half-mile from a ballfield on Eastern Avenue to a middle school softball field near the district’s administration building.

“A fair contract is a right, that is why we have to fight,’’ the demonstrators chanted as they walked along the sidewalk and passing cars beeped their horns.

Seeing hundreds turn out in support of Dedham’s schoolteachers and staff Saturday was overwhelming, said Kristen Mahoney, 40, who teaches fifth grade and has worked in the town’s schools since 2001.

She said she voted for the strike Thursday but hoped that a deal would be reached quickly so she and her colleagues could continue working.

“Yesterday and today have been surreal . . . it’s not part of the job,’’ she said. “I want nothing more than to be back in the classroom Monday morning.’’

Middle school nurse Jennifer Atkins, 49, who has been on the picket line, said the strike has been “anxiety-producing’’ for the school staff, who want to return to work.

“All we want to do is be at the school and take care of the kids,’’ she said, “and not do this.’’

The large turnout at Saturday’s rally made her hopeful that a deal can be reached quickly, she said.

“I do love my job, and I want to go back,’’ she said.

Jessica Walsh, 28, a paraprofessional at the middle school, where she works with eighth-graders. She is part of the union that is not on strike but backs her striking colleagues.

“I support the kids who need special education, so I should be here to support the teachers,’’ she said.

The strike has the support of teachers who work in other communities.

Ruth Levanoni, 53, lives in Dedham but is a teacher at Lexington High School. She came to the rally to show support for her Dedham colleagues and called on Dedham’s school administration to reach an agreement quickly so the community doesn’t become divided by a lengthy strike.

“We need to stand up,’’ she said. “And [the administration] needs to step up.’’

Natalya Betzig, 31, a Boston Public Schools teacher at the city’s Newcomers International Academy, also joined the Dedham rally.

“Teachers work incredibly hard, and they need a fair contract,’’ she said.

Erik Privert brought his 8-year-old son, Ellis, a Dedham third-grader, to Saturday’s rally to show that their town backs its teachers and wants to invest in children’s education.

Privert, 40, and his wife have two children — their daughter will enter kindergarten in two years — and they have been working to figure out child-care options should the strike continue.

But that doesn’t deter their support of Dedham’s educators.

“It’s a long-term issue of us setting a good situation for the teachers, for the kids,’’ he said. “If Monday comes and we don’t have child care, we’ll figure it out, keep going, and be back out here and doing everything we can.’’

Brian MacQuarrie, Travis Andersen, and John Ellement of the Globe staff contributed to this report. John Hilliard can be reached at john.hilliard@globe.com.